Help please I will mark brainliest
(a) Using Fermat's little theorem, show that 999 999 is divisible by 7.
(b) A number has digits that are all 9 and is divisible by 13. Show that
it is also divisible by 1001.

The ordered pair which makes both inequalities true is: D. (3, 0).

In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.

In order to determine ordered pair which makes both inequalities true, we would substitute the points into the inequalities as follows:

At (0, 0), we have:

y > -2x + 3  

0 > -2(0) + 3

0 > 3 (false).

y < x – 2

0 < 0 - 2

0 < -2 (false)

At (0, -1), we have:

y > -2x + 3  

-1 > -2(0) + 3

-1 > 3 (false).

y < x – 2

-1 < 0 - 2

-1 < -2 (false)

At (1, 1), we have:

y > -2x + 3  

1 > -2(1) + 3

1 > -1 (true).

y < x – 2

1 < 1 - 2

1 < -1 (false)

At (3, 0), we have:

y > -2x + 3  

0 > -2(3) + 3

0 > -3 (true).

y < x – 2

0 < 3 - 2

0 < 1 (true).

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Answer:

  30.70 ft

Step-by-step explanation:

For shadow problems, we make the assumption that an object's height and its shadow length are proportional.

The proportion for the two objects is ...

  height/shadow = pole/(22 ft) = (6 ft)/(4.3 ft)

Multiplying by 22 ft, we find the pole height to be ...

  pole = (22 ft)(6 ft)/4.3) ≈ 30.70 ft

The flagpole is about 30.70 feet tall.

Answer:

x ≈ 8.0

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos37° =  =  ( multiply both sides by 10 )

10 × cos37° = x , thus

x ≈ 8.0 ( to the nearest tenth )

does this help? :D

Answer:

(2, - 2 )

Step-by-step explanation:

4x - y = 10 → (1)

x - 4 = y → (2)

substitute x - 4 = y into (1)

4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1

4x - x + 4 = 10

3x + 4 = 10 ( subtract 4 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2 - 4 = y

- 2 = y

solution is (2, - 2 )

Answer:

x = 2 , y = -2

Step-by-step explanation:

I will use the elimination method :

4x-y = 10 - Equation Number 1

x-4 = y  - Equation Number 2

For the second equation we add 4 to both sides and subtract y from both sides :

x = y + 4

x - y = 4 - Let's call this equation number 3 :

Now we can subtract the equation 1 with 3 to eliminate y :

3x = 6

x = 2

Now we substitute this value into equation 2 to solve for y :

(2)-4 = y

y = -2

Substitute these values into equation 1 to verify :

4(2) - (-2) = 10

8 + 2 = 10

10 = 10

So these values must be correct

Hope this helped and have a good day

Answer:

373 feet

Step-by-step explanation:

Since the rate of the machine producing ribbon is proportional to time, we can determine the number of inches of ribbon in 8 hours by some quick operations.

There are 16 1/2 hours in 8 hours, so we can multiply 280 by 16.

[tex]280 *16=4480[/tex]

Now, we have the number of inches it can produce in an 8-hour work day. However, we must convert to feet since that is the form of measurement the question is asking for. We can do so by dividing by 12.

[tex]4480/12=373.33[/tex]

Therefore, the number of feet the machine can produce in an 8-hour work day is 373.

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Step-by-step explanation:

the other answer is correct.

a few add-ons :

1 ft = 12 in

30 minutes = 1/2 hour (as every hour has 60 minutes)

every hour has therefore 2 half hours.

1 hour = 2 × 1/2 hour

8 hours = 8 × 2 × 1/2 hours = 16 × 1/2 hour

so, in 16 times the amount of time (8 hours) the machine can produce 16 times the amount of ribbon (16 × 280 in).

16 × 280 = 4480 in

and because every 12 in is 1 ft, this is then

4480/12 = 373.3333333... ft

therefore, 373 is the right answer (rounded).

The table that has a constant average rate of change represents a linear function.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input.

When this rate is constant, the function is said to be linear, hence the table that has a constant average rate of change represents a linear function.

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Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x-9 = 2(x+23) or 5x-9 = 2x+46

Let' x be the "number."

"Five times a number decreased by nine" means: 5x - 9

"equal to twice the number increased by 23" means:  = 2(x+23)

Put them together:  5x-9 = 2(x+23)

5x-9 = 2(x+23)

5x-9 = 2x+46

[The formatting of the possible answers does not include parentheses nor algebraic symbols, making selection of a correct answer difficult. ]

i. 20 people

ii. 3 people

iii. 26 people

We have that;

3x + 5 people likes apples

3x + 5 people likes banana

2x + 15 people likes at least one of the fruits

The total number of people = 55

Let's find the value of x

3x + 5 + 2x + 15 = 55

5x + 20 = 55

5x = 55 - 20

5x = 35

x = 35/5

x = 7

i. People that likes banana only =  3x + 5 = 3 × 5 + 5 = 15 + 5 = 20 people

ii. None of the fruits = 55 - 2x + 15 = 55 - 3x + 5 - 3x + 5 = 55 - 26 +26

= 55 - 52

= 3 people

iii. At most one fruit = 55 - 2x + 15 = 55 - 2(7) + 15 = 55 - 29 = 26 people

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Answer:

f(5)=17

Step-by-step explanation:

if,f(x)=3x+2

Then,f(5)=3*5+2

f(5)=17

Answer: B

Step-by-step explanation:

Given:
36=<1.02D-31.2<=41

Solve the compound inequality for D:

36+31.2<=1.02D<=41+31.2

67.2<=1.02D<=72.2

65.9<=D<=70.8

Therefore, option (b) is correct answer

a = 3, b = 4, and c = 2

a + b = c

3 + 4 = 2

3a + 4b = 2c
       -4     -4
     3a = -6c
      3       3
       a = -2

3a + 4b = 2c
-3             -3
      4b = -1c
        4     4

The reason why people sometimes assume that the calculation 9 + 10 = 21 is as explained below.

We want to find out the reason why people say that; 9 + 10 = 21

Now, the way you have explained it is one way to look at it by utilizing number bases to play around with the figures to arrive at 21.

However, another way is to use algebra trick pattern which is;

9 can be expressed as 3 * 3

Also, 10 can be expressed as 5 * 2. Thus, we now have;

(3 * 3) + (5 * 2)

The applying properties of algebra to cross multiply gives;

(3 * 2) + (5 * 3)

= 6 + 15

= 21

Now, though your explanation arrived at 21 and mine also 21, but those are not correct mathematical methods as 9 + 10 must be equal to 19 and not 21.

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The complete similarity transformation is: triangle abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].​

From the figure, we have:

AB = 2 units

DE = 4 units

So, the scale factor (k) is:

k = DE/AB

k = 4/2

k = 2

Also, both shapes are on either sides of the x-axis, and they are equidistant from the x-axis.

This means that the triangle is reflected across the x-axis with no translation.

Hence, the complete similarity transformation is: abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].​

So, the scale factor is 2

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The method that Chris can use to make sure the segments in the pattern are all parallel is to treat AI as a single line that acts as a transversal for the lines that need to be parallel.

Within the set of lines which need to be parallel, the acute angles must be congruent.

Both angles CDE and EDF need to be 180° minus twice the measure of one of the congruent acute angles.

The pair of the acute angles previously within each of the two sets of parallel lines are corresponding.

The fact that the transversals go through endpoints, there are no alternate angles, interior or exterior because alternate angles are on opposite sides of the transversal.

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Answer:

1200

Step-by-step explanation:

Ok since the oldest was given 2/5, the middle was given 1/2, and the youngest was given the rest, that means the fraction that the youngest was given has to make 2/5 + 1/2 + ? = 1. So we have the equation: [tex]\frac{2}{5} + \frac{1}{2} + x = 1[/tex]. Now to add the fractions simply multiply 2/5 by 2/2 and multiply 1/2 by 5/5 To get the same denominator: [tex]\frac{4}{10} + \frac{5}{10}+x=\frac{9}{10}+x[/tex]. This means that x is 1/10 , because in adding 1/10 you get the whole 10/10. So 120 is one tenth of the entire prize. This means to get the entire prize you simply multiply by 10. This gives you the equation 120 * 10 = 1200

Answer:

Given :- ABCD is a square.

To proof :- AC = BD and AC ⊥ BD

Proof :- In △ ADB and △ BCA

AD = BC [ Sides of a square are equal ]

∠BAD = ∠ABC [ 90° each ]

AB = BA [ Common side ]

△ADB ≅ △BCA [ SAS congruency rule ]

⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]

In △AOB and △AOD

OB = OD [ Square is also a parallelogram therefore, diagonal of parallelogram bisect each other ]

AB = AD [ Sides of a square are equal ]

AO = AO [ Common side ]

△AOB ≅ △ AOD [ SSS congruency rule ]

⇒ ∠AOB = ∠AOD [ Corresponding parts of congruent triangles are equal]

∠AOB + ∠AOD = 180° [ Linear pair ]

∠ AOB = ∠AOD = 90°

⇒ AO ⊥ BD

⇒ AC ⊥ BD

Hence proved, AC = BD and AC ⊥BD

Two triangles are said to be congruent if they have similar properties. Thus the required options to complete the paragraph proof are:

a. angle 1 is congruent to angle 2.

b. alternate angles are congruent if two parallel lines are cut by a transversal.

c. [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]

The similarity property of two or more shapes implies that the shapes are congruent. Thus they have the same properties.

From the given diagram in the question, it can be deduced that

ΔABC ≅ ΔABE (substitution property of equality)

Given that EA is parallel to BD, then:

i. <2 ≅ <3 (corresponding angle property)

ii. <1 ≅ < 4 (alternate angle property)

Thus, the required options to complete the paragraph proof are:

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Answer:

The 3rd graph from the top.

Step-by-step explanation:

Just Like the story, the third graph goes up slowly and plateaus for the duration of a school day, then goes back down quicker than it went up.

Using an exponential function, we have that:

a) The equation is: [tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex].

b) The house will have a value of $1 million during the year of 2037.

c) The expected value on April 1, 2020, is of $621,520.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the parameters are given as follows:

A(0) = 600000, r = 0.058 each 2 years.

Hence the exponential function is:

[tex]A(t) = 600000(1 + 0.058)^{\frac{t}{2}}[/tex]

[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]

Item b:

It is the year 2019 + t, for which A(t) = 1000000, hence:

[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]

[tex]1000000 = 600000(1.058)^{0.5t}[/tex]

[tex](1.058)^{0.5t} = 1.6667[/tex]

[tex]\log{(1.058)^{0.5t}} = \log{1.6667}[/tex]

[tex]0.5t\log{1.058} = \log{1.6667}[/tex]

[tex]t = \frac{\log{1.6667}}{0.5\log{1.058}}[/tex]

[tex]t = 18.12[/tex]

The house will have a value of $1 million during the year of 2037.

Item c:

April 1, 2020 is one year and 3 months = 1.25 years after January 1, 2019, hence the value of the home will be given by:

[tex]A(t) = 600000(1.058)^{\frac{t}{2}}[/tex]

[tex]A(1.25) = 600000(1.058)^{\frac{1.25}{2}}[/tex]

A(1.25) = $621,520.

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Answer:

The linear equation for the line with an x - intercept at (-2,0) and y-intercept at (0,-3) is found as [tex]$y=-\frac{3}{2} x-3$[/tex].

Step-by-step explanation:

A condition is given that a line has an x- intercept at (-2,0) and y - intercept at (0,-3).

It is asked to find a linear equation satisfying the given condition.

Step 1 of 2

Determine the slope of the line.

The points of the intercepts of the line are given as (-2,0) and (0,-3). Next, the formula for the slope is given as,

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute -3&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 0&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]$$\begin{aligned}m &=\frac{-3-0}{0-(-2)} \\m &=\frac{-3}{2} \\m &=-\frac{3}{2}\end{aligned}$$[/tex]

Step 2 of 2

Write the equation in the slope-intercept form.

The slope-intercept form of a line is given as follows,

y=mx+b

The coordinates at the y- intercept is (0,-3). Now, as the y- coordinate is -3, so b=-3.

So, substitute -3 for b and [tex]$-\frac{3}{2}$[/tex] for m in the equation y=mx+b, and simplify to get the equation as follows,

[tex]$$\begin{aligned}&y=-\frac{3}{2} x+(-3) \\&y=-\frac{3}{2} x-3\end{aligned}$$[/tex]

This is the required linear equation.

The probability that a student takes art, given that the student takes music is 10.8%

In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.

For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."

Two events, A and B, are independent if

P(A ∣ B)=P(A)

P(A).P(B) = P(A ∩ B)

In the given question there are independent events.

Given:-

P(A) = Student takes both art and music = 0.9

P(B) = Student takes music = 0.12

P(A ∩ B) = student takes art, given that the student takes music

Thus by using the formula we get,

P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%

The probability that a student takes art, given that the student takes music is 10.8%

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Answer: 1344

Step-by-step explanation:

Using the Pythagorean theorem, if we consider the unknown leg of the base, we get that it has a length of 12.

So, the area of the base is 96.

Multiplying this by the height, we get the volume is 1344 cubic inches.

Answer:

Step-by-step explanation:

at first decreased by 60% now increased by 80%

100 - 60% = 40

40 + 80% =

40 + 40 :100 * 80 =

40 + 32 =

72

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The initial price in this scenario is > sh 276000 and was therefore sold at a loss.

This is a situation in which the selling price of goods or services is lower than the cost price.

We were told that the selling price is sh 276000 which is less than the initial(cost) price hence he ran at a loss during the business transaction.

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The equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]

From the question, we are to determine the equation of the line that passes through the given points

Using the formula

[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

From the give information,

[tex]x_{1} = 1 \\y_{1} = 1\\{x_{2} =5[/tex]

[tex]y_{2} = 6\\[/tex]

Putting the parameters into the formula,

[tex]\frac{y-1 }{x-1} =\frac{6-1}{5-1}[/tex]

[tex]\frac{y-1 }{x-1} =\frac{5}{4}[/tex]

∴ [tex]y-1 = \frac{5}{4}(x-1)[/tex]

Hence, the equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]

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Answer:

Graph of exponential rising up to the right, through the point (0, 2).

Step-by-step explanation:

I think you mean  f(x) = 3^x + 1.

When x = 0, 3^x = 1, so the graph of f(x) = 3^x will rise up to the right and pass through point (0. 1)

The + 1 translates the graph up 1 unit so

The graph of f(x) = 3^x + 1 passes through the point (0, 2).

The thing that best describes the values of x and y is option B; they will be real numbers greater than or equal to 0.

The real number refers to the union of both rational and irrational numbers that can have negative or positive values.

From the given information:

Peaches are being bought and sold for $2 per pound.

There is no negative value used here if x represents the number of pounds of peaches bought and y represents the total cost of the peaches.

Thus, a conclusion that can be reached as to the values of x and y is that they contain real numbers greater than or equal to 0.

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Answer:

im pretty sure its d

Step-by-step explanation:

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